Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory

Understand

We consider the entanglement entropy for a free $U(1)$ theory in $3 + 1$ dimensions in the extended Hilbert space definition.

• By taking the continuum limit carefully we obtain a replica trick path integral which calculates this entanglement entropy.
• The path integral is gauge invariant, with a gauge fixing delta function accompanied by a Faddeev-Popov determinant.
• For a spherical region it follows that the result for the logarithmic term in the entanglement, which is universal, is given by the $a$ anomaly coefficient.